結果
| 問題 |
No.2544 Many RMQ Problems
|
| コンテスト | |
| ユーザー |
 Misuki
|
| 提出日時 | 2023-12-31 18:11:13 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 210 ms / 2,000 ms |
| コード長 | 7,189 bytes |
| コンパイル時間 | 2,907 ms |
| コンパイル使用メモリ | 209,768 KB |
| 実行使用メモリ | 39,220 KB |
| 最終ジャッジ日時 | 2024-09-27 17:08:08 |
| 合計ジャッジ時間 | 6,823 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 25 |
ソースコード
#pragma GCC optimize("O2")
#include <algorithm>
#include <array>
#include <bit>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <compare>
#include <complex>
#include <concepts>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numbers>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <ranges>
#include <set>
#include <span>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <variant>
//#define int ll
#define INT128_MAX (__int128)(((unsigned __int128) 1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1)
#define INT128_MIN (-INT128_MAX - 1)
namespace R = std::ranges;
namespace V = std::views;
using namespace std;
using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
using tiii = tuple<int, int, int>;
using ldb = long double;
//#define double ldb
template<class T>
ostream& operator<<(ostream& os, const pair<T, T> pr) {
return os << pr.first << ' ' << pr.second;
}
template<class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N> &arr) {
for(const T &X : arr)
os << X << ' ';
return os;
}
template<class T>
ostream& operator<<(ostream& os, const vector<T> &vec) {
for(const T &X : vec)
os << X << ' ';
return os;
}
/**
* template name: MontgomeryModInt
* author: Misuki
* reference: https://github.com/NyaanNyaan/library/blob/master/modint/montgomery-modint.hpp#L10
* last update: 2023/11/30
* note: mod should be a prime less than 2^30.
*/
template<uint32_t mod>
struct MontgomeryModInt {
using mint = MontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 res = 1, base = mod;
for(i32 i = 0; i < 31; i++)
res *= base, base *= base;
return -res;
}
static constexpr u32 get_mod() {
return mod;
}
static constexpr u32 n2 = -u64(mod) % mod; //2^64 % mod
static constexpr u32 r = get_r(); //-P^{-1} % 2^32
u32 a;
static u32 reduce(const u64 &b) {
return (b + u64(u32(b) * r) * mod) >> 32;
}
static u32 transform(const u64 &b) {
return reduce(u64(b) * n2);
}
MontgomeryModInt() : a(0) {}
MontgomeryModInt(const int64_t &b)
: a(transform(b % mod + mod)) {}
mint pow(u64 k) const {
mint res(1), base(*this);
while(k) {
if (k & 1)
res *= base;
base *= base, k >>= 1;
}
return res;
}
mint inverse() const { return (*this).pow(mod - 2); }
u32 get() const {
u32 res = reduce(a);
return res >= mod ? res - mod : res;
}
mint& operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
mint& operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
mint& operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
mint& operator/=(const mint &b) {
a = reduce(u64(a) * b.inverse().a);
return *this;
}
mint operator-() { return mint() - mint(*this); }
bool operator==(mint b) {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
bool operator!=(mint b) {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
friend mint operator+(mint a, mint b) { return a += b; }
friend mint operator-(mint a, mint b) { return a -= b; }
friend mint operator*(mint a, mint b) { return a *= b; }
friend mint operator/(mint a, mint b) { return a /= b; }
friend ostream& operator<<(ostream& os, const mint& b) {
return os << b.get();
}
friend istream& operator>>(istream& is, mint& b) {
int64_t val;
is >> val;
b = mint(val);
return is;
}
};
using mint = MontgomeryModInt<998244353>;
/**
* template name: comb
* author: Misuki
* last update: 2023/01/22
* note: remember to call init() before using it.
*/
const int MAX = 1000001;
mint fac[MAX], facInv[MAX];
void init() {
fac[0] = 1;
for(int i = 1; i < MAX; i++)
fac[i] = fac[i - 1] * i;
facInv[MAX - 1] = 1 / fac[MAX - 1];
for(int i = MAX - 2; i >= 0; i--)
facInv[i] = facInv[i + 1] * (i + 1);
}
mint C(int a, int b) {
if (b < 0 or a < b)
return 0;
else
return fac[a] * facInv[b] * facInv[a - b];
}
/**
* template name: NTT
* reference: https://judge.yosupo.jp/submission/69896
* last update: 2023/12/04
* remark: MOD = 2^K * C + 1, R is a primitive root modulo MOD
* remark: a.size() <= 2^K must be satisfied
* some common modulo: 998244353 = 2^23 * 119 + 1, R = 3
* 469762049 = 2^26 * 7 + 1, R = 3
* 1224736769 = 2^24 * 73 + 1, R = 3
* verify: Library Checker - Convolution
*/
template<int32_t k, int32_t c, int32_t r, class Mint>
struct NTT {
using u32 = uint32_t;
static constexpr u32 mod = (1 << k) * c + 1;
static constexpr u32 get_mod() { return mod; }
static void ntt(vector<Mint> &a, bool inverse) {
static array<Mint, 30> w, w_inv;
if (w[0] == 0) {
Mint root = 2;
while(root.pow((mod - 1) / 2) == 1) root += 1;
for(int i = 0; i < 30; i++)
w[i] = -(root.pow((mod - 1) >> (i + 2))), w_inv[i] = 1 / w[i];
}
int n = ssize(a);
if (not inverse) {
for(int m = n; m >>= 1; ) {
Mint ww = 1;
for(int s = 0, l = 0; s < n; s += 2 * m) {
for(int i = s, j = s + m; i < s + m; i++, j++) {
Mint x = a[i], y = a[j] * ww;
a[i] = x + y, a[j] = x - y;
}
ww *= w[__builtin_ctz(++l)];
}
}
} else {
for(int m = 1; m < n; m *= 2) {
Mint ww = 1;
for(int s = 0, l = 0; s < n; s += 2 * m) {
for(int i = s, j = s + m; i < s + m; i++, j++) {
Mint x = a[i], y = a[j];
a[i] = x + y, a[j] = (x - y) * ww;
}
ww *= w_inv[__builtin_ctz(++l)];
}
}
Mint inv = 1 / Mint(n);
for(Mint &x : a) x *= inv;
}
}
vector<Mint> conv(vector<Mint> a, vector<Mint> b) {
int sz = ssize(a) + ssize(b) - 1;
int n = bit_ceil((u32)sz);
a.resize(n, 0);
ntt(a, false);
b.resize(n, 0);
ntt(b, false);
for(int i = 0; i < n; i++)
a[i] *= b[i];
ntt(a, true);
a.resize(sz);
return a;
}
};
NTT<23, 119, 3, mint> ntt;
signed main() {
ios::sync_with_stdio(false), cin.tie(NULL);
init();
int n, q; cin >> n >> q;
vector<mint> A(n + 1), B(n + 1);
for(int i = 0; i <= n; i++)
A[i] = fac[i], B[i] = facInv[n - i];
A = ntt.conv(A, B);
mint ans = 0;
for(int l = 1; l <= n; l++)
ans += (n - l + 1) * fac[n - l] * A[l + n];
cout << ans * mint((ll)n * (n + 1) / 2).pow(q - 1) * q << '\n';
return 0;
}